Question

the scatter plot and line of best fit below show the length of 14 peoples femur (the long leg bone in the thigh) and their height in centimeters. based on the line of best fit, what would be the predicted height for someone with a femur length of 45 cm?

Explanation:

Step1: Find the slope of the line of best fit

We have two points on the line of best fit: \((35, 138)\) and \((40, 151)\). The slope \(m\) is calculated using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
So, \(m=\frac{151 - 138}{40 - 35}=\frac{13}{5} = 2.6\).

Step2: Find the equation of the line

Using the point - slope form \(y - y_1=m(x - x_1)\) with the point \((35, 138)\) and \(m = 2.6\).
\(y-138=2.6(x - 35)\)
\(y-138=2.6x-91\)
\(y=2.6x + 47\)

Step3: Predict the height for femur length \(x = 45\)

Substitute \(x = 45\) into the equation \(y=2.6x + 47\).
\(y=2.6\times45+47\)
\(y = 117+47\)
\(y=164\)

Answer:

The predicted height for a femur length of 45 cm is 164 centimeters.